Until his dying day, Joseph Lieberman regarded the fact he did not become Vice President of the United States a “miscarriage of justice”.

Lieberman, who died at age 82 last week, was the first Jewish candidate on a major-party presidential ticket when he was chosen by Al Gore as his running mate in the 2000 election.

But that devastating, and in his eyes grossly unfair, loss to George W. Bush never prevented him working closely with Republicans, even endorsing his friend John McCain in his ill-fated run against Barack Obama.

Speaking at Lieberman’s funeral, former Vice President Gore praised his running mate for always choosing “reconciliation”, describing him as a “mensch” whose example modern politicians could learn much from.

Gore, recognising that there is no English equivalent for the Yiddish term, told mourners at a synagogue in Stamford, Connecticut, that they could find its meaning by looking at Lieberman.

“Those who seek its definition will not find it in dictionaries so much as they find it in the way Joe Lieberman lived his life: friendship over anger, reconciliation as a form of grace,” Gore said.

“We can learn from Joe Lieberman’s life some critical lessons about how we might heal the rancour in our nation today.”

Lieberman broke new ground for Jews in America simply by being so visibly Jewish and making his faith integral to his politics.

His youngest daughter, Hana Lowenstein, speaking at the funeral, said her father’s every decision was guided by his faith. Through tears, she said of him: “You were literally someone who was sanctifying God’s name by everything you did.” Lieberman’s family said he had died “due to complications from a fall”.

Lieberman supported Israel and called himself an “observant” Jew. His family kept a kosher home and attended Shabbat services. To avoid conveyances on a Sabbath, he once walked five miles across town to the Capitol to block a Republican attempt to cut Medicare spending after attending services in Georgetown.

Gore picked Lieberman, in no small part, because he was the first significant Democrat to rebuke Bill Clinton for his sexual relationship with Monica Lewinsky. Gore knew he had to step out from Clinton’s shadow.

But while Gore-Lieberman won 500,000 more votes than Bush-Cheney, no clear winner emerged in the Electoral College. After weeks of wrangling, it came down to Florida where fewer than 600 votes appeared to separate them. In a landmark decision, the Supreme Court halted the hand counting of 61,000 ballots that the vote tabulation machines had missed. The decision effectively handed the presidency to Bush.

In an interview with the New York Times last year for his own obituary, Lieberman said: “It was a miscarriage of justice on two levels.

“One was that the Florida Supreme Court had already ruled in our favour to continue the recounts, and the other was that it was an extrajudicial political decision made in the crisis of a transition of power, and out of line with precedents of the Supreme Court.”

Lieberman went on to seek the 2004 presidential nomination but withdrew from the race, believing that his support for the Iraq war had doomed him.

In 2006, he lost his own Democratic primary in Connecticut to an anti-war candidate, but then, in a surprise result, won the general election as a third-party independent.

His new free rein as an independent allowed Lieberman to attend the 2008 Republican National Convention where he endorsed his friend John McCain for the presidency. McCain had him vetted as a possible running mate but instead chose Sarah Palin.

Lieberman criticised Barack Obama, the then Democratic nominee, as “a gifted and eloquent young man” but warned that he was too inexperienced to be president.

McCain later admitted that he wished he had chosen Lieberman instead of Palin, who became a liability as her deep inexperience on the national stage showed.

During his Senate tenure from 1989 to 2013, Lieberman generally sided with the Democrats on domestic issues, like abortion choices and civil rights, and with the Republicans on foreign and defence policies.

In his farewell speech to the Senate in 2012, Lieberman bemoaned modern politics.

“It is the partisan polarisation of our politics which prevents us from making the principled compromises on which progress in a democracy depends, and right now, which prevents us from restoring our fiscal solvency as a nation,” he said.

Joseph Lieberman could never be accused of slavishly toeing the party line or of engaging in modish politics. His conscience and his faith were the higher powers he answered to. And that free-thinking, brave and independent, endeared him to an electorate that never made him Vice President, but certainly returned him to the Senate when his own party had abandoned him. The US public recognised that in Joe Lieberman they had a moral compass.